MMC2017Grade 10Divisions1
Easy
E1Whatis thesum ofthe10consecutiveintegers starting from 4?[85]
E2Findtheleast valueofxthat satisfies theinequality5−4x≤2.[3
4]
E3Thesidesof a triangle are 8, 12, and14 cm long. Anewtriangleisconstructed byjoining themidpoints
ofthesidesofthe first trianglewithsegments.Whatis theperimeterofthisnewtriangle?[17cm]
E4 Whatis theremainderwhen 1 −x+2x2−3x3isdivided byx+1?[7]
E5 Findthevaluesofxthat satisfythe equation ∣x∣+x=0.[x≤0]
E6Amap hasascaleof2cm is to5km. If a highwayis 28km,howlong isitin themap?[11.2cm]
E7Twochordsof a circleintersectinside it. Ifthesegments ofone chord are12and16cm long, andone
segmentofthesecond chordis 24cm,howlong is theother segmentofthesecond chord?[8 cm]
E8 Whatis thesum ofthe first 100 even positiveintegers? [10100]
E9Whatis theperimeterof a squarethatisinscribed in a circlewithcircumference 10πcm?[4√5 cm]
E10Two menarerepainting awall. Working alone, the first mancanfinish itin 10hours, andthesecond
man in 12hours.Working together,whatpart ofthewall cantheyrepaintin 2hours? [11
30]
EX Whatis the centerofthe circlewithequation x2+y2−4y=10?[(0,2)]
Average
A1The first term of a geometricsequence is10, andits thirdterm is 20.Whatisits fifth term?[40]
A2Thelegsof a right triangle are2and2√2cm long. Whatis theradius ofthe circlethatcircumscribes
thetriangle?[√3cm]
A3Whatis therangeofthe function f(x)=2x+4−2x2?[(−∞,9
2]]
A4 Whatis thesum of1−2+3−4+5−6+⋯+2017? [1009]
A5 Findthesolution setoftheinequalityx(x−4)(x+2)2≤0?[{−2}∪[0,4]]
AX Twofactors of a third-degree polynomialP(x)arex+2andx−4. IfP(0)=8 andP(1)=−9, findthe
remaining factorofP(x).[2x−1]
Difficult
D1Thelargeroftwoconcentric circleshas radius 8 cm. If a chordofthelargercirclehatis tangent tothe
smallercirclehaslength 4√14 cm,whatis theradius ofthesmallercircle?[2√2cm]
D2If0○≤θ≤180○and cosθ=−1
3,whatis sin θ+tanθ.[−4√2
3]
D3Solve forxin the equation √x+1+√x−1
√x+1−√x−1=3.[5
3]
D4 Find all ordered pairs (x,y)that satisfybothequationsx+y=4andy=2x2−x+2.[(−1, 5),(1,3)]
